In A&E, I suspect that most people would agree that giving personal information for the purposes of triage is ok. But that is very different from a visit to a GP in a non-emergency situation, probably in one's home town in a waiting room where there are people who know who you are. The GP has your medical information, and being asked for details about the reason for your visit is intrusive.
Many receptionists, particularly in hospitals, don't respect the need for privacy that some people have. They are behind glass (probably for their own safety) and you have to speak fairly loudly to give your name, DOB and first line of your address, as well as which clinic your appointment is in. Some of them even read it out for you to check, so 'Mrs D Dog, 123 High Street, Hometown, DOB 1/1/1910 to see Dr Smith about your haemorrhoids??
There may be reasons for this, but as I said above, it doesn't mean that we have to like it. I used to be confident that anything I told my GP would be confidential, but now there are so many paramedical roles, as well as numerous admin staff with access to records that I am not, and it is all but impossible to have anything removed - even if it is inaccurate the best you can hope for is to get a not attached to that effect.
Now that the dentist, the podiatrist, the pilates teacher and goodness knows who else know all sorts of details about their clients, there really is no such thing as doctor-patient confidentiality any more.